1. Edge Detection
Prof. B.A.Khivsara

2. What is Edge Detection?
Identifying points/Edges in a digital image at which the image brightness changes sharply or has discontinuities.
- Edges are significant local changes of intensity in an image.
- Edges typically occur on the boundary between two different regions in an image.

3. Goal of edge detection
Edge detection is extensively used in image segmentation when we want to divide the image into areas corresponding to different objects.
If we need to extract different object from an image, we need Edge Detection.
Using Edge Detection, we can- recognition, Image comparizon, Unaccepted object can be remove.

4. Variation of Intensity / Gray Level
TYPES OF EDGES
Variation of Intensity / Gray Level
Step Edge
Ramp Edge
Line Edge
Roof Edge

5. Process of Edge Detection
There are three steps to perform edge detection:
Noise reduction
Edge enhancement
Detection – Identify edges

6. Process of Edge Detection - Noise reduction
 where we try to suppress as much noise as possible, without smoothing away the meaningful edges.
Original Image
After Nois Reduction

7. Process of Edge Detection - Edge enhancement
where we apply some kind of filter that responds strongly at edges and weakly elsewhere.

8. METHODS OF EDGE DETECTION
First Order Derivative / Gradient Methods
Roberts Operator
Sobel Operator
Prewitt Operator
Second Order Derivative
Laplacian
Laplacian of Gaussian
Optimal Edge Detection
Canny Edge Detection

9. First Order Derivative
At the point of greatest slope, the first derivative has maximum value
E.g. For a Continuous 1-dimensional function f(t)

10. Gradient
For a continuous two dimensional function Gradient is defined as

11. Gradient Methods – Roberts Operator
Convolution Mask
Gx =
Gy= 1 -1 -1 1

12. Roberts Operator - Example
The output image has been scaled by a factor of 5
Spurious dots indicate that the operator is susceptible to noise

13. Gradient Methods – Sobel Operator
The 3X3 convolution mask smoothes the image by some amount , hence it is less susceptible to noise. But it produces thicker edges. So edge localization is poor
Convolution Mask 1 2 -1 -2 -1 1 -2 2
Gx=
Gy=

14. Sobel Operator - Example
Compare the output of the Sobel Operator with Roberts
The spurious edges are still present but they are relatively less intense
Roberts operator has missed a few edges
Sobel operator detects thicker edges
Outputs of Sobel (top) and Roberts operator

15. Second Order Derivative Methods
Zero crossing of the second derivative of a function indicates the presence of a maxima

16. Second Order Derivative Methods - Laplacian
Defined as
Mask
Very susceptible to noise, filtering required, use Laplacian of Gaussian 1 -4

17. Second Order Derivative Methods - Laplacian of Gaussian
Steps
Smooth the image using Gaussian filter
Enhance the edges using Laplacian operator
Zero crossings denote the edge location
Use linear interpolation to determine the sub-pixel location of the edge

18. Program
#Libraries to be installed # sudo apt-get install python-opencv # sudo apt-get install python-matplotlib import cv2 from matplotlib import pyplot as plt img0 = cv2.imread('images.jpeg',)# loading image gray = cv2.cvtColor(img0, cv2.COLOR_BGR2GRAY)# converting to gray scale img = cv2.GaussianBlur(gray,(3,3),0)
# remove noise cv2.GaussianBlur(image,(Kernal_Hieght,Kernal_Width),SigmaX)

19. Program
# convolute with proper kernels laplacian = cv2.Laplacian(img,cv2.CV_64F) sobelx = cv2.Sobel(img,cv2.CV_64F,1,0) # x sobely = cv2.Sobel(img,cv2.CV_64F,0,1) # y
plt.subplot(2,2,1),plt.imshow(img,cmap = 'gray') plt.title('Original'), plt.xticks([]), plt.yticks([]) plt.subplot(2,2,2),plt.imshow(laplacian,cmap = 'gray') plt.title('Laplacian'), plt.xticks([]), plt.yticks([]) plt.subplot(2,2,3),plt.imshow(sobelx,cmap = 'gray') plt.title('Sobel X'), plt.xticks([]), plt.yticks([]) plt.subplot(2,2,4),plt.imshow(sobely,cmap = 'gray') plt.title('Sobel Y'), plt.xticks([]), plt.yticks([]) plt.show()